Physics and Mirrors Help
The Convex Mirror
A convex mirror reflects light rays in such a way that the effect is similar to that of a concave lens. Incident rays, when parallel, are spread out (Fig. 19-8a ) after they are reflected from the surface. Converging incident rays, if the angle of convergence is just right, are collimated by a convex mirror (see Fig. 19-8b ). When you look at the reflection of a scene in a convex mirror, the objects all appear reduced. The field of vision is enlarged, a fact that is used to advantage in some automotive rear-view mirrors.
The extent to which a convex mirror spreads light rays depends on the radius of curvature. The smaller the radius of curvature, the greater is the extent to which parallel incident rays diverge after reflection.
The Concave Mirror
A concave mirror reflects light rays in a manner similar to the way a convex lens refracts them. When incident rays are parallel to each other and to the axis of the mirror, they are reflected so that they converge at a focal point (Fig. 19-9a ). When a point source of light is placed at the focal point, the concave mirror reflects the rays so that they emerge parallel (see Fig. 19-9b ).
The properties of a concave mirror depend on the size of the reflecting surface, as well as on the radius of curvature. The larger the light-gathering area, the greater is the light-gathering power. The smaller the radius of curvature, the shorter is the focal length. If you look at your reflection in a convex mirror, you will see the same effect that you would observe if you placed a convex lens up against a flat mirror.
Concave mirrors can have spherical surfaces, but the finest mirrors have surfaces that follow the contour of an idealized three-dimensional figure called a paraboloid . A paraboloid results from the rotation of a parabola , such as that having the equation y = x 2 in rectangular coordinates, around its axis. When the radius of curvature is large compared with the size of the reflecting surface, the difference between a spherical mirror and a paraboloidal mirror (more commonly called a parabolic mirror ) is not noticeable to the casual observer. However, it makes a big difference when the mirror is used in a telescope.
Physics and Mirrors Practice Problem
Suppose that a simple convex lens is made from the same material as a prism that casts a rainbow when white light is shone through it. How does the focal length of this lens for red light compare with its focal length for blue light?
The glass has a higher refractive index for blue light than for red light. Therefore, the glass bends blue light more, resulting in a shorter focal length for blue than for red.
Practice problems of these concepts can be found at: Optics Practice Test
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